Potential energy functions (PES) of AB4-type molecules which are constructed using ten symmetrised combinations of natural four A-Bi valence and six (A-Bi)(A-Bj) interbond angled are referred to as (10S) PESs. This set of coordinates is redundant with respect to the conventional set of 3N-6=9 vibrational degrees of freedom. At high energy ranges, it was found that (10S) PESs permitted improving by factor of five the fit quality of ab initio electronic energies of methane versus standard nine symmetric coordinates (9S) PES representations both in internal, orthogonal or normal-mode coordinates. We extend predictions of vibrational band origins to spectral range above 10000 cm -1 to help future analyses of experimental spectra. Accuracy at high energies is increased without notable deterioration at low-E levels (rms of 0.26 cm -1 ). Based on a comparison between various variants of (10S) PESs we expect that new theoretical band origins should have accuracy not worse than 1-3 cm -1 up to 13400 cm -1 .